Joint, or simultaneous, measurements of non-commuting observables are possible within quantum mechanics, if one accepts an increase in the variances of the jointly measured observables. In this paper, we discuss joint measurements of a spin 1/2 particle along any two directions. Starting from an operational locality principle, it is shown how to obtain a bound on how sharp the joint measurement can be. We give a direct interpretation of this bound in terms of an uncertainty relation.
Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality r…
Contextuality is a key resource in quantum information and the device-independent security of quantum algorithms. In this work, we show that the recently developed, operational Mermin non-locality arguments provide a large, novel family of quantum realisable All-vs-Nothing models. In particular, they result in a diverse wealth of quantum realisable models which are maximally contextual (i.e. lie on the faces of the no-signalling polytope with no local elements), and could be used as a resource for the security of a new class of quantum secret sharing algorithms.
In order to study N-locality without inputs in long lines and in configurations with loops, e.g. the triangle, we introduce a natural joint measurement on two qubits different from the usual Bell state measurement. The resulting quantum probability $p(a_1,a_2,...,a_N)$ has interesting features. In particular the probability that all results are equal is that large, while respecting full symmetry, that it seems highly implausible that one could reproduce it with any N-local model, though - unfortunately - I have not been unable to prove it.
Quantum non-locality is normally defined via violations of Bell's inequalities that exclude certain classical hidden variable theories from explaining quantum correlations. Another definition of non-locality refers to the wave-function collapse thereby one can prepare a quantum state from arbitrary far away. In both cases one can debate on whether non-locality is a real physical phenomenon, e.g. one can employ formulations of quantum mechanics that does not use collapse, or one can simply refrain from explaining quantum correlations via classical hidden variables. Here we point out that there …
We look at what type of arguments can rule out the joint reality (or value definiteness) of two observables of a physical system, such as a qubit, and give several strong yet simple no-go results based on assumptions typically weaker than those considered previously. The first result uses simple geometry combined with a locality assumption to derive device-independent steering inequalities. These may also be regarded as "conditional" Bell inequalities, are simpler in principle to test than standard Bell inequalities, and for two-qubit systems are related to properties of the quantum steering e…
We show an operational approach to bilocality with quasi-probability distributions and quasi-stochastic processes. This approach clearly demonstrates that negative probabilities are necessary to violate bilocality. It also highlights a subtle interplay between bilocal and local correlations and it can be easily extended to study N-locality.
An operational concept of locality whose quantum violation is indicated independently of any other assumption(s) seems to be lacking in the quantum foundations literature so far. Bell's theorem only shows that quantum correlations violate the conjunction of the ontological assumptions of localism and determinism. Taking a cue from computational complexity theory, here we define such a concept of locality in terms of a class of operational decision problems, and propose that Einstein-Podolsky-Rosen (EPR) steering in its basic asymmetric formulation gives a specific realization of this class. Va…
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed. Inside this reconstruction the measurement problem as well as the other major problems raised by the quantum mechanical formalism, dissolve.
Bell's theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of quantum mechanically incompatible quantities. We first recall several contradictions arising between the assumption of a joint distribution for incompatible observables and the probability structure of quantum-mechanics, and conclude that Bell's theorem is not expected to be relevant to quantum phenomena described by non-commuting observables, irrespective …
Does the remote measurement-disturbance of the quantum state of a system $B$ by measurement on system $A$ entangled with $B$, constitute a real disturbance -- i.e., an objective alteration -- of $B$ in an operational sense? Employing information theoretic criteria motivated by operational considerations alone, we argue that the disturbance in question is real for a subset of steerable correlations. This result highlights the distinction between quantum no-signaling and relativistic signal-locality. It furthermore suggests a natural reason why a convex operational theory should be non-signaling…
The debate on the nature of quantum probabilities in relation to Quantum Non Locality has elevated Quantum Mechanics to the level of an "Operational Epistemic Theory". In such context the quantum superposition principle has an extraneous non epistemic nature. This leads us to seek purely operational foundations for Quantum Mechanics, from which to derive the current mathematical axiomatization based on Hilbert spaces. In the present work I present a set of axioms of purely operational nature, based on a general definition of "the experiment", the operational/epistemic archetype of information …
Many of the contemporary formulations of quantum mechanics describe the marginal probability distributions of entangled many-body systems in a non-local way. Unlike the non-locality of joint distributions, the non-locality of marginal distributions is not forced by theory or experiment. This paper investigates the issue in the context of the Copenhagen, de Broglie-Bohm and sum-over-paths interpretations. A dissociation between information flow into quantum subsystems and the tensor product structure of wavefunctions is highlighted in connection to the problem.
Studying generalized non-local theories brings insight to the foundations of quantum mechanics. Here we focus on non-locality swapping, the analogue of quantum entanglement swapping. In order to implement such a protocol, one needs a coupler that performs the equivalent of quantum joint measurements on generalized `box-like' states. Establishing a connection to Bell inequalities, we define consistent couplers for theories containing an arbitrary amount of non-locality, which leads us to introduce the concepts of perfect and minimal couplers. Remarkably, Tsirelson's bound for quantum non-locali…
The insight due to John Bell that the joint behavior of individually measured entangled quantum systems cannot be explained by shared information remains a mystery to this day. We describe an experiment, and its analysis, displaying non-locality of entangled qutrit pairs. The non-locality of such systems, as compared to qubit pairs, is of particular interest since it potentially opens the door for tests of bipartite non-local behavior independent of probabilistic Bell inequalities, but of deterministic nature.
We introduce a framework for studying non-locality and contextuality inspired by the path integral formulation of quantum theory. We prove that the existence of a strongly positive joint quantum measure -- the quantum analogue of a joint probability measure -- on a set of experimental probabilities implies the Navascues-Pironio-Acin (NPA) condition $Q^1$ and is implied by the stronger NPA condition $Q^{1+AB}$. A related condition is shown to be equivalent to $Q^{1+AB}$.
The framework of generalized probabilistic theories (GPT) is a widely-used approach for studying the physical foundations of quantum theory. The standard GPT framework assumes the no-restriction hypothesis, in which the state space of a physical theory determines the set of measurements. However, this assumption is not physically motivated. In Janotta and Lal [Phys. Rev. A 87, 052131 (2013)], it was shown how this assumption can be relaxed, and how such an approach can be used to describe new classes of probabilistic theories. This involves introducing a new, more general, definition of maxima…
Two parts of an entangled quantum state can have a correlation in their joint behavior under measurements that is unexplainable by shared classical information. Such correlations are called non-local and have proven to be an interesting resource for information processing. Since non-local correlations are more useful if they are stronger, it is natural to ask whether weak non-locality can be amplified. We give an affirmative answer by presenting the first protocol for distilling non-locality in the framework of generalized non-signaling theories. Our protocol works for both quantum and non-qua…
Topological systems, such as fractional quantum Hall liquids, promise to successfully combat environmental decoherence while performing quantum computation. These highly correlated systems can support non-Abelian anyonic quasiparticles that can encode exotic entangled states. To reveal the non-local character of these encoded states we demonstrate the violation of suitable Bell inequalities. We provide an explicit recipe for the preparation, manipulation and measurement of the desired correlations for a large class of topological models. This proposal gives an operational measure of non-locali…
An examination is made of the differing implications from applying the two mainstream interpretations of probability, frequentist and Bayesian, to QM (quantum mechanics) theory for the Bohm-EPR experiment. The joint probability distribution for the possible spin outcomes for two particles with coupled spins is examined. Contrasting conclusions are made: (i) Under the frequentist interpretation, the QM spin distribution implies a widely-discussed non-locality because probabilistic conditioning on a spin measurement is viewed as corresponding to a causal influence. Under the Bayesian interpretat…
We highlight the existence of a joint probability distribution as the common underpinning assumption behind Bell-type, contextuality, and Leggett-Garg-type tests. We then present a procedure to translate contextual scenarios into temporal Leggett-Garg-type and spatial Bell-type ones. To demonstrate the generality of this approach we construct a family of spatial Bell-type inequalities. We show that in Leggett-Garg scenario a necessary condition for contextuality in time is given by a violation of consistency conditions in Consistent Histories approach to quantum mechanics.
Non-local correlations are usually understood through the outcomes of alternative measurements (on two or more parts of a system) that cannot altogether actually be carried out in an experiment. Indeed, a joint input/output -- e.g., measurement-setting/outcome -- behavior is non-local if and only if the outputs for all possible inputs cannot coexist consistently. It has been argued that this counterfactual view is how Bell's inequalities and their violations are to be seen. We propose an alternative perspective which refrains from setting into relation the results of mutually exclusive measure…
Passive light-source side channel in quantum key distribution (QKD) makes the quantum signals more distinguishable thus provides additional information about the quantum signal to an eavesdropper. The explicit eavesdropping strategies aimed at the passive side channel known to date were limited to the separate measurement of the passive side channel in addition to the operational degree of freedom. Here we show how to account for the joint eavesdropping on both operational degree of freedom and the passive side channel of the generic form. In particular, we use the optimal phase-covariant clon…
We introduce a framework for simulating quantum measurements based on classical processing of a set of accessible measurements. Well-known concepts such as joint measurability and projective simulability naturally emerge as particular cases of our framework, but our study also leads to novel results and questions. First, a generalisation of joint measurability is derived, which yields a hierarchy for the incompatibility of sets of measurements. A similar hierarchy is defined based on the number of outcomes used to perform the simulation of a given measurement. This general approach also allows…
Some new Bell inequalities for consecutive measurements are deduced under joint realism assumption, using some perfect correlation property. No locality condition is needed. When the measured system is a macroscopic system, joint realism assumption substitutes the non-invasive hypothesis advantageously, provided that the system satisfies the perfect correlation property. The new inequalities are violated quantically. This violation can be expected to be more severe than in the case of precedent temporal Bell inequalities. Some microscopic and mesoscopic situations, in which the new inequalitie…
Marginal problems naturally arise in a variety of different fields: basically, the question is whether some marginal/partial information is compatible with a joint probability distribution. To this aim, the characterization of marginal sets via quantifier elimination and polyhedral projection algorithms is of primal importance. In this work, before considering specific problems, we review polyhedral projection algorithms with focus on applications in information theory, and, alongside known algorithms, we also present a newly developed geometric algorithm which walks along the face lattice of …
Two physical principles, Macroscopic Locality (ML) and Information Causality (IC), so far, have been most successful in distinguishing quantum correlations from post-quantum correlations. However, there are also some post-quantum probability distributions which cannot be distinguished with the help of these principles. Thus, it is interesting to see whether consideration of these two principles, separately, along with some additional physically plausible constraints, can explain some interesting quantum features which are otherwise hard to reproduce. In this paper we show that, in a Bell-CHSH …
Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, o…
In quantum mechanics, joint measurements of non-commuting observables are only possible if a minimal unavoidable measurement uncertainty is accepted. On the other hand, correlations between non-commuting observables can exceed classical limits, as demonstrated by the violation of Bell's inequalities. Here, the relation between the uncertainty limited statistics of joint measurements and the limits on expectation values of possible input states is analyzed. It is shown that the experimentally observable statistics of joint measurements explain the uncertainty limits of local states, but result …
This talk is a survey of the question of joint measurability of coexistent observables and its is based on the monograph Operational Quantum Physics [1] and on the papers [2,3,4].
Oblivious transfer, a central functionality in modern cryptography, allows a party to send two one-bit messages to another who can choose one of them to read, remaining ignorant about the other, whereas the sender does not learn the receiver's choice. Oblivious transfer the security of which is information-theoretic for both parties is known impossible to achieve from scratch. - The joint behavior of certain bi-partite quantum states is non-local, i.e., cannot be explained by shared classical information. In order to better understand such behavior, which is classically explainable only by com…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The question is answered as to when the consecutive applications of measuring apparatuses give a simultaneous measurement of their observables. For this purpose, all the possible state reductions caused by measurements of an observable is also characterized by their operations.
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify uncertainty (and joint uncertainty). In this paper we use operational information-theoretic principles to identify the common essence of all such measures, thereby defining measure-independent notions of uncertainty and joint uncertainty. We find that most existing entropic uncertainty relations use measures of joint uncertainty that yield themselves to a s…
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational quantity, namely the probability of distinguishing the actual operation of a device from its hypothetical ideal, by any possible testing procedure whatsoever. Moreover, they may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information …
We introduce an operational discord-type measure for quantifying nonclassical correlations in bipartite Gaussian states based on using Gaussian measurements. We refer to this measure as operational Gaussian discord (OGD). It is defined as the difference between the entropies of two conditional probability distributions associated to one subsystem, which are obtained by performing optimal local and joint Gaussian measurements. We demonstrate the operational significance of this measure in terms of a Gaussian quantum protocol for extracting maximal information about an encoded classical signal. …
We show that different entropic measures of fluctuations lead to contradictory uncertainty relations for two complementary observables. We apply Tsallis and Rényi entropies to the joint distribution emerging from a noisy simultaneous measurement of both observables as well as to the product of their individual statistics, either intrinsic or of operational origin.
Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, we establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity. In particular, we establish a direct connection between Mermin-type non-locality scenarios, which we generalise to an arbitrary number of parties, using systems of arbitrary dimension, and performing arbitrary measurements, and a new stronger notion of complementarity which we introduce here. Our derivation of the fact that strong complementarity is a nece…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle relative to the von Neumann chain. For the basis of the theory, the local measurement theorem provides the joint probability distribution for the outcomes of local successive measurements on a noninteracting entangled system without assuming the projection postulate, and the quantum Bayes principle enables us to determine operationally the quantum state from a …
We discuss a novel framework for physical theories that is based on the principles of locality and operationalism. It generalizes and unifies previous frameworks, including the standard formulation of quantum theory, the convex operational framework and Segal's approach to quantum field theory. It is capable of encoding both classical and quantum (field) theories, implements spacetime locality in a manifest way and contains the complete modern notion of measurement in the quantum case. Its mathematical content can be condensed into a set of axioms that are similar to those of Atiyah and Segal.…
Quantum theory puts forward phenomena unexplainable by classical physics - or information, for that matter. A prominent example is non-locality. Non-local correlations cannot be explained, in classical terms, by shared information but only by communication. On the other hand, the phenomenon does not allow for (potentially faster-than-light) message transmission. The fact that some non-local and non-signaling correlations are predicted by quantum theory, whereas others fail to be, asks for a criterion, as simple as possible, that characterizes which joint input-output behaviors are ``quantum'' …
In order to analyze joint measurability of given measurements, we introduce a Hermitian operator-valued measure, called $W$-measure, such that it has marginals of positive operator-valued measures (POVMs). We prove that ${W}$-measure is a POVM {\em if and only if} its marginal POVMs are jointly measurable. The proof suggests to employ the negatives of ${W}$-measure as an indicator for non-joint measurability. By applying triangle inequalities to the negativity, we derive joint measurability criteria for dichotomic and trichotomic variables. Also, we propose an operational test for the joint me…
The definition of memory in operational approaches to quantum non-Markovianity depends on the statistical properties of different sets of outcomes related to successive measurement processes performed over the system of interest. Using projectors techniques we develop a perturbation theory that enables to expressing both joint probabilities and outcome correlations in terms of the unperturbed system density matrix propagator. This object defines the open system dynamics in absence of measurement processes. Successive series terms, which are scaled by the system-environment interaction strength…
Here we focus on the measurement induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement induced nonlocality and has analytic expressions for many quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost analytic expressions for any quantum state, which can also shed light…
Operational Concealment of Measurement Incompatibility by Quantum Channels: Rank Loss versus Contraction
Jawaharlal Nehru Rajkeeya Mahavidyalaya（贾瓦哈拉尔·尼赫鲁国立学院）；University of Electronic Science and Technology of China（电子科技大学）；Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学前沿科学技术研究院）
